GCD of 414, 380, 48, 462 Calculator

Given Input numbers are 414, 380, 48, 462

To find the GCD of numbers using factoring list out all the divisors of each number

Divisors of 414

List of positive integer divisors of 414 that divides 414 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

Divisors of 380

List of positive integer divisors of 380 that divides 380 without a remainder.

1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380

Divisors of 48

List of positive integer divisors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Divisors of 462

List of positive integer divisors of 462 that divides 462 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462

Greatest Common Divisior

We found the divisors of 414, 380, 48, 462 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 414, 380, 48, 462 is 2.

Therefore, GCD of numbers 414, 380, 48, 462 is 2

Given Input Data is 414, 380, 48, 462

Make a list of Prime Factors of all the given numbers initially

Prime Factorization of 414 is 2 x 3 x 3 x 23

Prime Factorization of 380 is 2 x 2 x 5 x 19

Prime Factorization of 48 is 2 x 2 x 2 x 2 x 3

Prime Factorization of 462 is 2 x 3 x 7 x 11

Highest common occurrences in the given inputs are 2¹

Multiplying them we get the GCD as 2

Step1:

Let's calculate the GCD of first two numbers

The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)

LCM(414, 380) = 78660

GCD(414, 380) = ( 414 x 380 ) / 78660

GCD(414, 380) = 157320 / 78660

GCD(414, 380) = 2

Step2:

Here we consider the GCD from the above i.e. 2 as first number and the next as 48

The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)

LCM(2, 48) = 48

GCD(2, 48) = ( 2 x 48 ) / 48

GCD(2, 48) = 96 / 48

GCD(2, 48) = 2

Step3:

Here we consider the GCD from the above i.e. 2 as first number and the next as 462

The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)

LCM(2, 462) = 462

GCD(2, 462) = ( 2 x 462 ) / 462

GCD(2, 462) = 924 / 462

GCD(2, 462) = 2

GCD of 414, 380, 48, 462 is 2

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1. What is the GCD of 414, 380, 48, 462?

GCD of 414, 380, 48, 462 is 2

2. Where do I get the detailed procedure to find GCD of 414, 380, 48, 462?

You can find a detailed procedure to find GCD of 414, 380, 48, 462 on our page.

3. How to find GCD of 414, 380, 48, 462 on a calculator?

You can find the GCD of 414, 380, 48, 462 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.